John Cantwell

When a belief set is contracted only some beliefs are eligible for removal. By introducing eligibility for removal as a new semantic primitive for contraction and combining it with epistemic entrenchment we get a contraction operator with a number of interesting properties. By placing some minimal constraint upon eligibility we get an explicit contraction recipe that exactly characterises the so called interpolation thesis, a thesis that states upper and lower bounds for the amount of information to be given up in contraction. As a result we drop the controversial property of recovery. By placing additional constraints on eligibility we get representation theorems for a number of contraction operators of varying strength. In addition it is shown that recovery contraction is a special case that we get if eligibility is explicitly constructed in terms of logical relevance.

A semantics is presented for belief revision in the face of common announcements to a group of agents that have beliefs about each other’s beliefs. The semantics is based on the idea that possible worlds can be viewed as having an internal-structure, representing the belief independent features of the world, and the respective belief states of the agents in a modular fashion. Modularity guarantees that changing one aspect of the world (a belief independent feature or a belief state) has no effect on any other aspect of the world. This allows us to employ an AGM-style selection function to represent revision. The semantics is given a complete axiomatisation (identical to the axiomatisation found by Gerbrandy and Groeneveld for a semantics based on non-wellfounded set theory) for the special case of expansion.

The problems that surround iterated contractions and expansions of beliefs are approached by studying hypertheories, a generalisation of Adam Grove's notion of systems of spheres. By using a language with dynamic and doxastic operators different ideas about the basic nature of belief change are axiomatised. It is shown that by imposing quite natural constraints on how hypertheories may change, the basic logics for belief change can be strengthened considerably to bring one closer to a theory of iterated belief change. It is then argued that the logic of expansion, in particular, cannot without loss of generality be strengthened any further to allow for a full logic of iterated belief change. To remedy this situation a notion of directed expansion is introduced that allows for a full logic of iterated belief change. The new operation is given an axiomatisation that is complete for linear hypertheories.

This paper provides finitary jointly necessary and sufficient acceptance and rejection conditions for the logical constants of a first order quantificational language. By introducing the notion of making an assignment as a distinct object level practice—something you do with a sentence—(as opposed to a meta-level semantic notion) and combining this with the practice of (hypothetical and categorical) acceptance and rejection and the practice of making suppositions one gains a structure that is sufficiently rich to fully characterize the class of classical first order theories. The analysis thus provides a way of characterizing classical first order quantification by expressivist means.

A semantics is presented for belief revision in the face of common announcements to a group of agents that have beliefs about each other’s beliefs. The semantics is based on the idea that possible worlds can be viewed as having an internal-structure, representing the belief independent features of the world, and the respective belief states of the agents in a modular fashion. Modularity guarantees that changing one aspect of the world (a belief independent feature or a belief state) has no effect on any other aspect of the world. This allows us to employ an AGM-style selection function to represent revision. The semantics is given a complete axiomatisation (identical to the axiomatisation found by Gerbrandy and Groeneveld for a semantics based on non-wellfounded set theory) for the special case of expansion.

The view that decision methods can only be justified by appeal to pragmatic considerations is defended. Pragmatic considerations are viewed as providing the underlying subject matter (“semantics”) of decision theories. It is argued that other approaches (e.g. justifying principles by appeal to obviousness, common usage, etc.) fail to provide grounds for a normative decision theory.It is argued that preferences that can lead to pragmatically adverse outcomes in a relevantly similar possible decision situation are pragmatically unsound, even if the decision situation never arises. This rebuts several standard objections to money-pump and Dutch book arguments. However, because one can only appeal to relevantly similar decision situations in pragmatic arguments, these will have a less general scope than is often imagined. A conclusion is that pragmatic arguments for strong unconditional principles such as ‘always maximise expected utility!’ do not work. Pragmatic considerations can however be used to argue for conditional principles of the form ‘if conditions X, Y and Z are satisfied, then one ought to satisfy W’, where W need not follow logically from X, Y and Z.The notion of a sound pragmatic argument is defined in terms of particular notion of coherence, it is shown how this can be applied and how it handles problematic cases such as van Fraassen’s Dutch book for the principle of Reflection.

Ever since [4], systems of spheres have been considered to give an intuitive and elegant way to give a semantics for logics of theory- or belief- change. Several authors [5, 11] have considered giving up the rather strong assumption that systems of spheres be linearly ordered by inclusion. These more general structures are called hypertheories after [8]. It is shown that none of the proposed logics induced by these weaker structures are compact and thus cannot be given a strongly complete axiomatization in a finitary logic. Complete infinitary axiomatizations are given for several intuitive logics based on hypertheories that are not linearly ordered by inclusion.

A formal model for updates—the result of learning that the world has changed—in a multi-agent setting is presented and completely axiomatized. The model allows that several agents simultaneously are informed of an event in the world in such a way that it becomes common knowledge among the agents that the event has occurred. The model shares many features with the model for common announcements—an announcement about the state of the world in which it becomes common knowledge among the audience that the announcement has been made—presented in Cantwell (2005), but exploits the difference between learning that a state of the world obtains and learning that the state of the world has changed.